Question

Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine
(i) A × B (ii) B × A (iii) Is A × B = B × A ? (iv) Is n (A × B) = n (B × A) ?(v) B-A​

Answer 1

Answer:

Since A = {1, 2, 3, 4} and B = {5, 7, 9}.

Therefore,

(i) A × B = {(1, 5), (1, 7), (1, 9), (2, 5), (2, 7), (2, 9), (3, 5), (3, 7), (3, 9), (4, 5), (4, 7), (4, 9)}

(ii) B × A = {(5, 1), (5, 2), (5, 3), (5, 4), (7, 1), (7, 2), (7, 3), (7, 4), (9, 1), (9, 2), (9, 3), (9, 4)}

(iii) No, A x B ≠ B x A. Since A x B and B x A do not have exactly the same ordered pairs.

(iv) n (A x B) = n (A) x n (B) = 4 x 3 = 12

n(B x A) = n(B) x n(A) = 4 x 3 = 12

Hence, n(A x B) = n(B x A)

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

A = {1,2,3,4}

B = {5,7,9}

(i) A×B = {(1,5),(1,7),(1,9),(2,5),(2,7),(2,9),(3,5),(3,7),(3,9),(4,5), (4,7),(4,9)}

(ii) B×A = {(5,1),(5,2),(5,3),(5,4),(7,1),(7,2),(7,3),(7,4),(9,1),(9,2),(9,3),(9,4)}

(iii) A×B is not equal to B×A because the ordered pairs in both the sets are different.

(iv) n(A×B) = n(B×A)

Because n(A×B) = n(A)×n(B)

= 4×3

= 12

And n(B×A) = n(B)×n(A)

= 4×3

= 12

Therefore, n(A×B) = n(B×A)

(v) B-A = B intersection A'

= {5,7,9} intersection {5,7,9}

= {5,7,9} i.e. B

Hope it helps.